Claims

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1956_01_01_erdos_fuchs: Theorem 1 of Erdős and Fuchs (1956) proves that no sequence has its pair count equal to cn plus o(n^{1/4} (log n)^{-1/2}) with c > 0, so a bounded error is impossible; accepted, refereed and credited by the site.

1990_01_01_montgomery_vaughan: Montgomery and Vaughan (1990), after Jurkat, prove that no sequence has its pair count equal to cN plus o(N^{1/4}) with c > 0, ruling out a bounded error; accepted on the site's credit, the volume's refereeing undocumented.

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